Introduction to Algebra Flashcards

Study Notes

Variable: A letter or symbol representing a quantity that can change within mathematical expressions.
Constant: A fixed quantity that does not vary.
Algebraic Expression: A combination of one or more variables and constants linked by operation symbols (e.g., addition, subtraction).

Evaluate: The process of substituting a specific number for a variable in an expression and simplifying to find its value.
Equation: A mathematical assertion that asserts two quantities are equal, often containing variables.
Solution: A specific value of a variable that satisfies an equation and makes it valid.

Inverse Operations: Operations that reverse the effect of each other, such as addition and subtraction or multiplication and division.
Order of Operations: A prescribed sequence for evaluating mathematical expressions:
- Parentheses first
- Exponents second
- Multiplication and division from left to right
- Addition and subtraction from left to right

Commutative Property: Demonstrates that the order of addition or multiplication does not influence the result; e.g., a + b = b + a.
Associative Property: Indicates that the grouping of numbers does not affect the sum or product when adding or multiplying; e.g., (a + b) + c = a + (b + c).
Distributive Property: When distributing multiplication over addition, multiplying a sum by a number yields the same result as multiplying each addend individually and then summing them; expressed as a(b + c) = ab + ac.

Identity Property: Defines that adding zero to a number yields the number itself, and multiplying a number by one results in the number unchanged.

Exponent: A notation that signifies how many times a base is multiplied by itself.
Base: The number being multiplied in an exponential expression.
Exponential Form: Expressing numbers using a base and an exponent to indicate repeated multiplication.